1.3.2 Ordinal Variables

As with the nominal scale, the name of this scale is indicative of it’s defining feature: an order. That is, the categories of an ordinal variable cannot just be ordered arbitrarily in any other way, like we can with nominal variables, no: the categories of any ordinal variable have an inherent order to them. Listing the categories of an ordinal variable differently would violate the intrinsic logic of their order and would make little to no sense; as well, we would lose the information contained in their order.

Think back to the variable educational attainment from the  Do It! 1.2. exercise earlier. Educational attainment is usually measured by the educational degrees attained by an individual, so if you imagined the categories being something like no degree, secondary/high school, Associate’s, Bachelor’s, Master’s, doctorate/PhD you are probably not alone. That is, chances are, most, if not everyone, would come up with a list in that particular order. Why? Because, I can hear you explaining, no degree is the lowest formal educational attainment one can have; it’s clearly less than having finished secondary/high school, which in turn is less than having a college degree, which again is clearly less than achieving a Master’s degree, while, finally, a PhD is the highest degree one can get in academia. Arbitrarily switching the categories in educational attainment to be listed as, say, Associate’s, Master’s, no degree, PhD, Bachelor’s makes little (rather, no) sense, and worse, it deprives us of the information about there being an intrinsically ascending order in the obtaining of the degrees (as one can only have a doctorate if they had previously finished college, which ca only be done after secondary/high school). 

Note that having an intrinsic order (in this case, from less to more), however, is a necessary but not a sufficient condition to identify an ordinal scale. There is an additional requirement: a variable is ordinal only when the categories do not have a precise (numerical) value. In other words, while we know that a Bachelor’s degree is more than an Associate’s degree, we don’t know how much more. Having a PhD is more than a Master’s degree, but again, we don’t know by how much. The same goes for any of the categories. We know the order, but not the precise “distance” between one category and another. As well, the “distance” between the first category and the second one might be unequal (while still unknown) to the “distance” between the second category and the third, and so on. It is not the size of the distance that matters here, only that the distance exists and that a category is clearly less/more (or bigger/smaller, nearer/farther, etc.) than another.^[1]

To summarize: As you can see from this example, the key feature of ordinal variables is the intrinsic logical ordering of their categories, a logic that would be lost if we were to reorder them in any other way. As well, this tells you that ordinal variables contain more information in comparison to nominal variables: namely, the ordering of the ordinal variable’s categories. Ordering the categories of a variable is an additional action you can do above simply listing them. Finally, the general order is the only additional information: the “distances” between the categories could vary and should not be measurable/ quantifiable. If the latter is not the case, you are already moving into interval/ratio scales territory.